The museum, housed in two rooms on the second floor of New Scotland Yard, holds a collection of grisly artefacts relating to some of the most notorious cases of the past two centuries: death masks of convicts hanged at Newgate; the ricin pellet that killed Bulgarian dissident Georgi Markov in 1978; even the stove on which serial killer Dennis Nilsen boiled his victims.

Although there's no publicly available catalogue, its star piece is thought to be the "Dear Boss" letter, allegedly sent by Jack the Ripper to the Central News Agency in 1888. Its authenticity is disputed but, whatever the sender's real identity, the letter has a central place in Ripper mythology and therefore in our conceptions of crime and the criminal.

The group's vision for the museum is described in History's Life Sentence (PDF) – a report published this month. Its author, assembly member Roger Evans, proposes that the Met contract a private exhibition organiser to create a temporary show of the museum's most important pieces, with the proceeds (a hastily estimated £4m) going directly to frontline policing.

The report makes it clear that this is about making money: the cultural value of the collection is barely mentioned; the word "interpretation" is entirely absent. Which is perhaps why the proposal has been greeted with suspicion by many in the museum sector. The Met itself appears to have rejected it outright. But does Evans have a point, however crassly made?

In 2015 the Met will move to its new home in Whitehall. Now does seem a good time to debate the future of its collection and consider the question of public access. If the Met can be convinced to open up the museum, there are some tricky ethical questions it would have to tackle first.

"What's most important for a public museum with such a controversial collection is to be self-reflective and transparent about its mission and values," says Janet Marstine, director of museum and gallery studies at Leicester University and author of the Routledge companion to museum ethics. "If it aims to be socially purposeful and uses its collections to explore the complexities and contradictions of crime through history, then it may have an important contribution to make."

Rachel Cockett, a Birmingham museum worker who sits on the museum association's ethics committee, says the challenge is to avoid sensationalism without being dull and overly didactic. "Striking the appropriate balance in marketing material is important but informed sensitive interpretation is not a barrier to attracting audiences," she says. "A controversial object may draw a visitor in but high quality engagement and interpretation should mean they leave having had a meaningful experience."

As a trustee of the Birmingham Conservation Trust – which is currently restoring a coffin fitting factory in the city – Cockett has first hand experience of dealing with death and tragedy in a heritage setting. "Providing people with a comfortable environment and allowing for humour, curiosity and natural responses are essential," she explains.

But is it ever possible to display an object such as the Dear Boss letter without a sense of exploitation – and without being co-opted into the 'Ripper industry', through which a misogynistic killer has become something of a folk hero? "Jack the Ripper is so embedded within popular culture that he's almost become a fictional character," says Philip Stone, who leads the University of Central Lancashire's Institute for Dark Tourism Research. "The problem for the museum is that he clearly wasn't fictitious – he was real, there were real victims and murder is a tragedy."

One way to acknowledge that tragedy, Stone says, is to find innovative ways to explore the stories of the victims – not just those of the perpetrators. "The duty of care comes in telling a balanced story and not sensationalising it," he says. "The key question is: how do you differentiate between a museum and a visitor attraction? That's the line that's becoming increasingly blurred."

Museums have long understood the power of death and brutality to get visitors through the doors and cash in the till. But the best institutions have also allowed us to engage with difficult histories and the complex moral questions they raise. Crime and punishment are such emotive issues because they are central to how we understand society. With curatorial skill and sensitivity (rather than the assembly members' get-rich-quick approach) the Met's collection could offer an unrivalled opportunity to reflect on them.

James Gray is a freelance journalist – follow him on Twitter @james_gray_